I eventually found that 32-Bit application support is disabled by default in IIS7 on 64-Bit, so to resolve the error, here is what I needed to do:

Create a new Application Pool using Internet Information Services (IIS) Manager by clicking “Application Pools” on the left hand pane. Click “Add Application Pool” and provide it with a name such as “Classic ASP”. Right click the new application pool and select “Advanced Settings” and under “General” switch “Enable 32-Bit Applications” to “True”.

Then switch your ASP site over to use the new Application Pool by right clicking on the site name and selecting “Manage Application”/”Advanced Settings” and changing the Application Pool to the newly created “Classic ASP”.